有理Toeplitz矩阵的极限eigenvalue分布的平衡问题
An equilibrium problem for the limiting eigenvalue distribution of rational Toeplitz matrices
摘要：
本文研究了有理符号Toeplitz矩阵特征值随矩阵大小趋于无穷大的渐近性态。我们的主要结果是，弱极限的归一化特征值计数措施是一个特殊的组件的唯一解决方案的向量平衡问题。此外，我们表明，其他组件描述某些广义本征值的极限行为。这样，我们推广了Duits和Kuijlaars关于带状Toeplitz矩阵的近期结果.
英文摘要：
We consider the asymptotic behavior of the eigenvalues of Toeplitz matrices with rational symbol as the size of the matrix goes to infinity. Our main result is that the weak limit of the normalized eigenvalue counting measure is a particular component of the unique solution to a vector equilibrium problem. Moreover, we show that the other components describe the limiting behavior of certain generalized eigenvalues. In this way, we generalize the recent results of Duits and Kuijlaars for banded Toeplitz matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
